Understanding Qualitative Robust Stability of Composite Variational Systems

Abstract The main objective of this paper is to study the Lipschitz-like stability property, in particular the Aubin property, of the solution map for potentially nonmonotone variational systems with composite structure. Using the Mordukhovich coderivative criterion and second-order subdifferential analysis, we derive simple and geometrical characterizations of this property based on the data involved in the problem. Applications of these theoretical results are given in the context of market pricing strategies in economics. Furthermore, we explore Julia and Ipopt solver to compute the Lipschitz modulus of the solution map around a reference point, showing the practical implementation of our results.